The Harmony Learning Community Blog

News, Updates, Program Recaps, and Homeschooling Information

Registration Open for Math Circle

Talking Stick’s popular Math Circle will be back again this year, and registration is now open! Mt. Airy mathematician Rodi Steinig, our Math Circle founder and facilitator since 2011, has worked tirelessly over the summer months to prepare some amazing programs for this year, including: Modular Arithmetic for age 5 What is a Number? for ages 6 & 7 The…

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PROOFS #7: We Want to Think

(May 28, 2013)  Seventy-five minutes.  No future sessions.  Four kids.  Five proofs.  What to do? This was the dilemma facing our Math Circle today.  I’d been deliberating all week over how best to use our last session.  So many proofs.  So little time. I gave the decision to the kids in attendance, R, P, N, and G.  Our options:  a…

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PROOFS #5: Debating the Merits of Proofs

  THEOREM:          A cat has nine tails. PROOF:                1.  No cat has 8 tails.                                 2.  One cat has one more tail than no cats.  Therefore, a cat has nine tails.1 (May 14, 2013)  We began today’s Math Circle debating the merits of the cat-has-nine-tails “proof.”  N stood at the board diagramming “my” reasoning.  G came up to…

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PROOFS #2: Exponents, Roots, Pythagoras, Theorems, Proofs, and The Kaplans

PROOFS #2:  Exponents, Roots, Pythagoras, Theorems, Proofs, and The Kaplans [juicebox gallery_id=”25″] (April  23, 2013) Before continuing our TV problem, the students recapped last session for A, who had been absent last week.  This week’s problem solving once again presented rich opportunities for delving deeply into arithmetic; it has not been the algebra and geometry that is challenging for these…

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Math Circle Blog: Signaling Problem Solution via Proof by Contradiction

Signaling Problem Solution via Proof by Contradiction December 11, 2012: We began our final session of our Signalling Problem Math Circle with a few rounds of Exploding Dots, this time in binary.  The large number of explosions in binary (base two) compared to decimal (base ten) was such fun.  I asked the group how many different numbers could be represented…

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Math Circle Blog: Plato, Codes, and Exploding Dots

Plato, Codes, and Exploding Dots “I must add how charming the science of arithmetic is and in how many ways it is a subtle and useful tool to achieve our purposes, if pursued in the spirit of a philosopher, and not of a shopkeeper!’” This was the last line of a dialogue my assistant R and I read at the…

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Math Circle Blog: Popcorn, Nose Rings, and Parameters

This Week Our Group Invents Parameters. SEPTEMBER 25, 2012: Here’s what I expected to happen in Math Circle today: The students would walk in, discuss A’s discovery of an important calculation error last week, and then continue the Popcorn Problem. I had placed unpopped popcorn kernels on the table before I told them the life story of Enrico Fermi. Hopefully,…

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Math Circle Blog: The Kaplans on Algorithms

“The idea of a Math Circle is to not tell anyone anything.” So began the Math Circle Summer Teacher Training Institute, led by Bob and Ellen Kaplan. Bob continued:  “To discover and construct mathematics for yourself is to make it yours.  You can use it again and again.”  Throughout the week, new and experienced Math Circle leaders practiced telling kids…

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More Than One Way to Enjoy Math

The 60 seconds of disorder in out classroom reveals something about how people enjoy math: different people enjoy it in different ways. We all have what the Kaplan’s refer to as “the architectural instinct” – a natural desire to pursue revelations about structure. But some of us seek structure numerically, others geometrically, others logically, and so on.

In our group, different styles are emerging, and it will be fun to see if and how they change over time.